1, A population of values has a normal distribution with=95.8 and=77.4. You intend to draw a random sample of sizen=10.

Find the probability that a single randomly selected value is less than 120.3.

P(X< 120.3) =

Find the probability that a sample of sizen=10n=10is randomly selected with a mean less than 120.3.

P(x< 120.3) =Enter your answers as numbers accurate to 4 decimal places.

2, A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 267.1-cm and a standard deviation of 1.9-cm. For shipment, 12 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 266.1-cm.

P(x< 266.1-cm) =

Enter your answer as a number accurate to 4 decimal places.

3, CNNBC recently reported that the mean annual cost of auto insurance is 1030 dollars. Assume the standard deviation is 248 dollars. You take a simple random sample of 55 auto insurance policies.

Find the probability that a single randomly selected value is less than 979 dollars.

P(X< 979) =

Find the probability that a sample of sizen=55is randomly selected with a mean less than 979 dollars.

P(x< 979) =

Enter your answers as numbers accurate to 4 decimal places.

4, Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 124000 dollars. Assume the standard deviation is 43000 dollars. Suppose you take a simple random sample of 72 graduates.

Do not use probability tables to find the probabilities below as they may not be accurate enough.

Find the probability that a single randomly selected salary exceeds 119000 dollars.

P(X> 119000) =

Find the probability that a sample of sizen=72is randomly selected with a mean that exceeds 119000 dollars.

P(x> 119000) =

Enter your answers as numbers accurate to 4 decimal places.

5, A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 144.8-cm and a standard deviation of 0.8-cm. For shipment, 16 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 144.3-cm.

P(x> 144.3-cm) =

Enter your answer as a number accurate to 4 decimal places.

6, CNNBC recently reported that the mean annual cost of auto insurance is 970 dollars. Assume the standard deviation is 183 dollars. You will use a simple random sample of 115 auto insurance policies.

Find the probability that a single randomly selected policy has a mean value between 1007.5 and 1017.8 dollars.

P(1007.5 <X< 1017.8) =

Find the probability that a random sample of sizen=115has a mean value between 1007.5 and 1017.8 dollars.

P(1007.5

Enter your answers as numbers accurate to 4 decimal places.

7, A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 231.5-cm and a standard deviation of 1.5-cm. For shipment, 21 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 231.4-cm and 232-cm.

P(231.4-cm

Enter your answer as a number accurate to 4 decimal places.

8, The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.933 g and a standard deviation of 0.325 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. In what range would you expect to find the middle 50% of amounts of nicotine in these cigarettes (assuming the mean has not changed)?

Between and. (Enter your answers in ascending order...smaller on left, larger on right. Also, enter your answers accurately to four decimal places.)

If you were to draw samples of size 48 from this population, in what range would you expect to find the middle 50% of most average amounts of nicotine in the cigarettes in the sample?

Between and.(Enter your answers in ascending order...smaller on left, larger on right. Also, enter your answers accurately to four decimal places.)

9, Finance4U magazine researched the salaries of employees of a tech company in Portland. They took a sample of 63 salaries. They discovered the average yearly salary to be $146,000. Assume a population standard deviation of $37,000.

Be sure to watch the video linked in the problem to see how to write up your work using proper notation, defining variables, etc.

A, What is the standard deviation of the sampling distribution for this situation? Round to four places. Show work and answer using proper notation.

B, Find the probability that a single randomly selected salary has a value between $140,406 and $152,992. Your write up should include all of the following:

• Define therandom variableyou are using.
• Use correct notation to label all quantities.
• State or show how you found your final probability. You can use tables or StatCrunch, just specify what you did.
• Show your answer using full and correct probability notation. Round to four places.
• State your final result in a complete-sentence form, with correct context, numbers and units.

C, Find the probability that a random sample of sizen=63has a mean value between $140,406 and $152,992.

• Define therandom variableyou are using.
• Use correct notation to label all quantities.
• State or show how you found your final probability. You can use tables or StatCrunch, just specify what you did.
• answer using full and correct probability notation. Round to four places.
• State your final result in a complete sentence form, with correct context, numbers, and units.